Question

The following except which are accurate of the coefficient of determination?which is correct?

r²indicates a causal relationship where r indicates only an association, y explains as much of x as x explains of y, coefficient of determination values are equal-interval scores, The coefficient of determination is a measure of effect size

Answer 1

ANSWER:-

"R^2" indicates the causal relationship and "r" indicates only association,y explains x and x explains y.

EXPLANATION:-

Correlation

A correlation is a measure or degree of relationship between two variables. A set of data can be positively correlated, negatively correlated or not correlated at all. As one set of values increases the other set tends to increase then it is called a positive correlation.

As one set of values increases the other set tends to decrease then it is called a negative correlation.

If the change in values of one set doesn't affect the values of the other, then the variables are said to have "no correlation" or "zero correlation."

In the model correlation means association between dependent variable as well as the independent variable.i.e.how x explains y and vice-versa.

the measure of effect is all about explained by correlation.

Causation

A causal relation between two events exists if the occurrence of the first causes the other. The first event is called the cause and the second event is called the effect. A correlation between two variables does not imply causation. On the other hand, if there is a causal relationship between two variables, they must be correlated.

In the similar fashion how the independent variable affect the dependent variable is causation.the coefficient of determination measures the effect of independent variable on the dependent variable.

Example:

A study shows that there is a negative correlation between a student's stress before a test and the student's score on the test. But we cannot say that the stress causes a lower score on the test; there could be other reasons—the student may not have studied well. So the correlation here does not imply causation.

However, consider the positive correlation between the number of hours you spend studying for a test and the grade you get on the test. Here, there is causation and correlation both if you spend more time studying, it results in a higher grade.

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